Velocity Feedback Control of Swing Phase for 2-DoF Robotic Leg Driven by Electro-hydraulic Servo System

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1 Enneen ee, 4:4, E_4_4_ eloy Feeba onol of Swn hae fo -DoF obo e Den by Eleo-hyaul Seo Syem Jan Zhan, e Yu an e Dn ba Th ae een a omuaonal moel fo a nonlnea wo eee-of-feeom -DoF obo le. The moel bae on a mahemaal moel of wo onnee boy emen o mm he lowe hh an han of human le. Two e of eleo-hyaul eo yem ESS ae eeaely ue o e he obo hh an han. The ynam of ESS auaely eeloe o ehb he elaonh of he nu uen an he auae foe\oue. eloy obee ue o emae he anula eloe of he obo hh an han. Then, a eloy feeba onolle ooe o a he h an nee jon moemen of obo le. The mulaon eul how ha he eloy feeba onolle e bee an efomane n em of oon onol aey when omae wh he onenonal ID onolle. Ine Tem obo le, Eleo-hyaul eo yem, eloy feeba onolle, ID onolle. T I. INTODUTION he e mehanm wh a wo eee-of-feeom -DoF e ha been wely ue a mehanal ool n he nuy manufaue, nlun obo yem, njeon mahne an bon mahne 3. Geneally, he auaon fo a -DoF e elee o be moo o eleohyaul eo yem ESS. Many eeahe an alaon of moo hae been mae o onol he -DoF e 4 6. owee, n h ae, he ealzaon of -DoF n ehnoloe ahee by ulzn wo e of ESS fo he ably of hh loa effeny, fa eone, an hh an auay 7. The moeln of ESS eemely fful fo ome nonlnea me-ayn henomena, uh a he elaonh beween nu uen an ouu flow, flu omebly, eaban ue o he nenal leaae an eenal loa 8. In aon, he alue of hyaul aamee may ay ue o emeaue hane an a enamen n he hyaul flu. Bae on he ee objee, onol aee fo ESS an be lafe a oon onol 9, eloy onol 3 an foe/oue onol 4 5. Fo any one of he onol aee, he onolle en wll ely affe he an efomane of ESS. Geneally, he ID onolle mo wely ue ue o mle onol uue, eae of en an low o 6. owee, he ID onolle omleely neenen of he mahemaal moel of ESS. In h ae, a -DoF obo le noue whh en by ESS fo boh he obo hh an han. The moeln fo obo le an ESS bul bae on he anfomaon of aane euaon an flu euaon. onally, he eloy emae un an obee an he eloy feeba onolle ooe houh he aual oon an emae eloe. The mulaon eul how ha he ooe eloy feeba onolle oe le an la an le mean abolue eo ME han he onenonal ID onolle. II. METOD In h eon, he ynam moel ae eaaely ee fo he ESS an -DoF obo le. Th analy maly bul he nonlnea moel of he ESS ynam, an how he oe of he auao n he obo le. Smla aoahe o moeln of ESS hae been eoe n 7 8. The -DoF obo le une oneaon afe n F.. The obo le on of wo a nlun hh an han. Two e of ESS ae lae o e he obo hh an han. Manu eee Febuay 8 h, 6. Th wo wa uoe by he Naonal Naual Sene Founaon of hna une Gan No an Euaonal ommon of ube one of hna une Gan No. 36. Jan Zhan now wh ollee of omue Sene, Yanze Uney, JnZhou, hna. e-mal: zhanjan76@6.om. e Yu wh he Shool of Eleon an Eleal Enneen, Wuhan Tele Uney, Wuhan, hna. oeonn auho o oe hone: ; e-mal: honyeal@whu.eu.n. e Dn wh he Shool of Infomaon an Enneen, Wuhan Uney of Tehnoloy, Wuan, hna. e-mal: @.om. F.. Shema Daam of he ESS an -DoF obo le ane onlne ublaon: 6 Noembe 6

2 Enneen ee, 4:4, E_4_4_. Moeln of obo e The ynam of -DoF obo le an be onue by aane euaon a follow:, G T In 9, he an ae ee an eeloe bae on he ouble emen omoun enulum an aane euaon. owee, he ee fomula of nlue he eeon of, an he ee fomula of nlue he eeon of. The ouln of an an no be nelee. Bae on h, we ue he anfomaon of aane euaon o elmnae he neelaonh beween an. T, G whee - G G G T T T 3 whee, an G ae he nea ma, ool ma an ay eo, eeely, T an T ae he oue auae eeally on lowe hh an han. θ an θ ae he oay anle of hh an han a hown n F.. The elemen of ma -, an G an be eee a follow: noe noe 4m 4I - 44I - 44I m o m noe m o m noe 44I 4m 4m o m m 4I 4I m noe m 6I I 4m 6m I m 4m I - 4m o -m -o n n o G - m -o n n o G G m -o n n o G m Gn - m-n - G n m G n G 4 whee m he hh ma, m he han ma, he hh lenh, he han lenh, G he he oon of he ene of he hh ma, G he he oon of he ene of he han ma, I he hh nea an I he han nea. The an an be obane un he anfomaon of aane euaon n E.. owee, he eeon n E. 4 e ha he,, an houl alo be aue. Fo mulaon, he,, an an be wen a:.5.5 B. Moeln of Eleo-yaul Seo Syem hown n F., wo e of ESS eneae he foe\oue o e he obo hh an han. Fo he ESS, he n oue T an be alulae a: T F 6 whee T T T F F F 7 whee F he n foe fo he obo hh jon, F he n foe fo he obo han jon, an ae he hea-e eue of hyaul fo he obo hh an han, eeely; an ae he o-e eue of hyaul fo he obo hh an han, eeely; he hea-e aea; he o-e aea; an ae he am of foe fo he obo hh an han, eeely. Due o he eomey of he obo yem, he an an be omue a: abn a b abn 8 o o whee a, b, an ae he eomey lenh of he obo hh an han a hown n F.. In E. 7, he an an be alulae houh he follown fomula when he boe amee D an he o amee D ae aue. D 4 9 D D 4 he he o amee D een le han he boe amee D, he E. 5 an be mlfe a D D D 4 4 Subun he E. no E. 7, he auae foe an be mlfe a F F F Nelen he eenal leaae, he eue ynam n auao hambe an be ebe a 5 ane onlne ublaon: 6 Noembe 6

3 whee = +, = -, = +, = - ae he onol olume of he auao hambe, hambe olume uh ha a =, = = o =, = = ; β he effee bul moulu n he hambe; an ae he loa eloy of he obo hh an han, eeely; = - an = - ae he loa eue of he ynam auao of he obo hh an han, eeely; he oeffen of he oal nenal leaae of he auao ue o he eue; an ae he ule flow ae o he fowa hambe, an an ae he eun flow ae of he eun hambe.,, an ae elae o he ool ale laemen of he eo-ale. 3 whee w 4 efne a f f 5 whee he ale hae an, he hae oeffen, w he ool ale aea aen, ρ he eny of hyaul ol, he uly eue of he flu, an he eun eue. owee, he,, an an be alulae a o n o n o n ab b a ab ab b a 6 whee he ylne ea lenh an he on oon when he olume ae eual on boh ylne e. Sne a hh-eone eo ale ue, aume ha he uen ale o he eo ale ely ooonal o he ool oon, hen he follown euaon en by =, whee a oe eleal onan, an he nu uen. Thu, fom E., =. Then E. 3 an be ewen a 7 whee = an 8 Bae on he E. an 8, we hae 9 Theefoe, he eaon of he auae foe F an F an be obane by F F F In aal won onon, he,, an ae all boune by an,.e. < < <, < < <, < < < an < < <. In mulaon oe, he an ae boh boune by,.e. - < < an - < <. III. ONTOE DESIGN The am of he onolle o ealuae he an efomane of ESS uh ha he ee an aual oon houl be obane befoe onolle en. In h ae, he ee oon θ an θ ae ene o be he oay anle of human h an nee jon n one a yle. Then, he onolle en an be mae a a amln feueny of f=z o eamne he behao of he yem.. Den of he ID onolle To e he oon an efomane of -DoF obo le en by ESS, a feeba onolle ae no h yem whee he aual oon.e., θ an θ of hh an han ae hen omae wh he ee oon efne n E.. The eo beween he ee oon an aual oon alulae an fe ba o he yem. The eue oue o omenae hee eo ae eneae by he nu uen no he eo ale, whh ae fue ou by a ooonal-ineal-deae ID onolle fo boh lowe hh an han a hown n E.. F. lluae he blo aam fo he onenonal ID onolle ha ae o he nonlnea -DoF obo le yem. The onenonal ID onolle an be onue a follow. e e e whee Enneen ee, 4:4, E_4_4_ ane onlne ublaon: 6 Noembe 6

4 Enneen ee, 4:4, E_4_4_ e - e e - whee an ae he nu uen no he ale of hh an han a een n E. 9, eeely., an ae he fe ooonal, neal an ffeenal an fo he obo hh, eeely., an ae he fe ooonal, neal an ffeenal an fo he obo han, eeely. F.. The blo aam of he ID onolle heme B. Den of he eloy Feeba onol Fo he onenonal ID onolle, he anula eloe ae obane un he eleal neaon meho a hown n E. 5. In h ae, we ae ue of an obee o emae he anula eloe. The obee an be wen a ˆ z 3 z ˆ whee ˆ z ˆ z ˆ z 4 whee z an z ae he obee ae; an ae he obee an o enue oneene of he eo o zeo; ˆ an ˆ ae he emae anula eloy of he hh an han. The emae eloy an be ue n he feeba loo of he oon onolle o eeae he an eo. The ooe onolle obane houh an a eloy eo em o a ooonal onolle, whh hown n he blo aam of F. 3. The onol law an be eee a ˆ 5 whee ˆ ˆ ˆ 6 whee α, β, α an β ae fe onolle an. In fa, h onolle a ae feeba onolle whee he eloy em eeen he nenal ae of he auaon yem. I. SIMUTION ESUTS. Seleon of Syem aamee In oe o emonae he effeene of h yem, he ESS an he -DOF obo le ae mulae wh he follown nomnal aamee: m =7, m =3.6, =.43m, =.5m, G =.4m, G =.8m, I =.3 m, I =.7 m, =.77-4 m, a=.4m, b=.6m, =.7m, =.8m, = 6 a, =.5 5 a, =.m, =.8m, β= 7 a, =.5-4 m 3, =8 - m 5 N - -, = m 4 - N -/. B. Seleon of Obee Gan To eablh onon on he an o enue he obee ably, we one he eo beween he aual eloy an emae ˆ. ˆ 7 e Dffeenan boh e of he aboe euaon yel an analy eeon ha ebe he ae of hane of he eo e. Fom he E. 4, he ffeenal euaon of he eo e eee a e z ˆ ˆ 8 To mae he obee able o be ue n he ESS an -DOF obo le, he yauno funon houl be afe ha ee ˆ ˆ ˆ 9 The eleon of obee an mu be obeye ha >. fe mae al, he omum of obee an mae ha =3 an =5.. Seleon of onolle Gan The an of he onenonal ID onolle ae hoen un Zele-Nhol meho. Then, omum an of =6, =4 an =5 ae obane fo he onolle o a he oon of he obo hh. In aon, he an fo he onolle o ae he be oon an of he obo han ae elee ha =, =4 an =3. The omal alue fo he an of he eloy feeba onolle ae mae ha α =6, β =65, α = an β =6. D. omaon eul Beween he ID onolle an eloy Feeba onolle The yem mulaon an be mlemene by Malab bae on he noue ESS moel an mahemaal -DOF obo le moel. The omue mulaon ae onue un wo ye of onolle, uh a ID onolle an eloy fee ba onolle. F. 3. The blo aam of he eloy feeba onolle heme ane onlne ublaon: 6 Noembe 6

5 Enneen ee, 4:4, E_4_4_ n F. 7 an F. 8, he emae eloy un obee moe mooh omae wh ha un neal way. F. 4. Tan efomane fo obo le: a Dee moemen fo obo le, b ual moemen un ID onolle, ual moemen un eloy feeba onolle The ee moemen fo -DOF obo le ae emonae n F. 4a, whle F. 4b an F. 4 e he aual moemen un he ID onolle an eloy feeba onolle, eeely. owee, he onol effe fo boh onolle an no be onee a omaable eul. In oe o lay he onolle effe omaaely, he onolle efomane ae nae by he mean abolue eo ME an an la. F. 7. The aue eloy fo obo h: a Thouh neal way, b Thouh obee emaon F. 8. The aue eloy fo obo nee: a Thouh neal way, b Thouh obee emaon F. 5. Tan efomane fo obo h un: a ID onolle, b eloy feeba onolle F. 6. Tan efomane fo obo nee un: a ID onolle, b eloy feeba onolle F. 5 how, he onol efomane fo obo h un eloy feeba onolle oban le ME.7 a an le an la 8 m han ha un ID onolle ME=.34 a, an la=8 m. on o he ME an la alue laye n F. 6, un he eloy feeba onolle ME=.65 a, an la =7 m eul n euon of oon eo an an la omae wh he ID onolle ME=.88 a, an la =8 m. The omaae eul ue ha he eloy feeba onolle e bee efomane fo -DOF obo le. Fo eloy feeba onolle, he eloy emae un an obee a een n E. 3. owee, he eloy aue un neal way fo ID onolle. ebe. ONUSION mahemaal an omuaonal moel of -DOF obo le en by ESS ha been uefully eeloe, mulae an ee n MTB ofwae. The aoah o mm he lowe hh an han emen of he human le onal an unue o ue he mahemaal one an he aane euaon o ahee he yem ynam. In aon, he eloy feeba onolle ooe o a he oon ajeoy of -DOF obo le, whle an obee ue o emae he eloy. Two ye of onolle, uh a he onenonal ID onolle an he eloy feeba onolle, ae aen o oban omaae eul. omae wh he ID onolle, he mulaon eul how ha he ooe eloy feeba onolle aue le ME an le an la n em of oon onol aey. NOWEDGMENT Th eeah uoe an fune by ube Dal Manufaun ey aboaoy an ey aboaoy of Fbe O Senn Tehnoloy an Infomaon oen. We alo han he anonymou eewe an eo fo he aluable ommen an ueon. EFEENES. J. Meeen, J. J.. aule, an E.. omonoa, naly an en oneaon of a -DOF oay-lnea auao, n o. IEEE In. Ele. Mah. De onf., ,.. Bolone, noel oay-lnea emanen mane ynhonou mahne un ommon ae a, n o. 5h IEEE Meeanean Eleoeh. onf., ,. 3 J.. S,.. Fen,. W., Y.. u, Den an naly of a -DOF Sl-Sao Inuon Moo, IEEE Tanaon on eney oneon, ol. 3, no. 3,. -8, 5. ane onlne ublaon: 6 Noembe 6

6 Enneen ee, 4:4, E_4_4_ 4. J. Meeen, J. J.. aule, an E.. omonoa, naly of a noel manezaon aen fo -DoF oay-lnea auao, IEEE Tan. Man., ol. 48, no., ,. 5 E.. Menela an E. Geza, Double-wnn oay-lnea nuon moo, IEEE Tan. Eney one., ol. E-, no., , J. Fleza an E.. Menela, Twn-amaue oay-lnea nuon moo, IEEE o. B, ol. 3, no. 3,. 86 9, J.. Gao an. D. Wu, fuzzy neual newo onolle n he eleohyaul oon onol yem, IEEE nenaonal onfeene on nellen yem, 997, Oobe 8-3; Bejn, hna. 8.. wan, Neual-Newo-Bae aable Suue onol of Eleohyaul Seoyem Subje o hue uneane whou een eaon, IEEE/SME Tanaon on mehaon, ol. 4, no.,. 5-59, F. Sa,. Sa, F. Djeffal, an M. Meuella, "Moeln, onol an Omzaon of a New Swmmn Moobo Den," Enneen ee, ol. 4, no.,. 6-, 6. E. Dee, n nellen oon onol of eleohyaul e un hyb fuzzy onol uue, oeen of he IEEE Inenaonal Symoum on Inual Eleon., ol.3,. 8-3, 999. T.. hen an Y.. Wu, n omal aable uue onol wh neal omenaon fo eleohyaul oon eo onol yem, IEEE anaon on nual eleon., ol. 39, no. 5, , a,. Nuyen, D.. ye an. F. Duan-Whye, Sln moe onol wh fuzzy unn fo eleohyaul oon eo yem, 998 eon nenaonal onfeene on nowlee-bae nellen eleon yem, l, G. aanfa, M.. Zaf an.. Ghaee, Nonlnea obu baen onol of an eleohyaul eloy eo yem, Meeanean onfeene on onol an auomaon, July, 7 4 S. Tafazol,. W. e Sla an. D. awene, Tan onol of an elehyaul manulao n he eene of fon, IEEE Tanaon on onol yem ehnoloy, May, S. Tafazol,. W. e Sla an. D. awene, Fon emaon n a lana eleohyaul manulao, oeen of he mean onol onfeene, Seale, mean, June.. 4-4, Zhona Tan, Shujan, Yanhon Wan, an uan Zhan, "Mul emanen Mane Synhonou Moo Synhonzaon onol bae on aable Unee Fuzzy I Meho," Enneen ee, ol. 3, no.3,. 8-88, 5. 7 J. Y. Yao, Z. X. Jao an S. S. an, Fon omenaon fo low eloy onol of hyaul flh moon mulao: mle aae obu aoah, hnee Jounal of eonau., ol. 6, no. 3,. 84-8, 3. 8 J. Y. Yao, Z. X. Jao an B. YO, obu onol fo Sa oan of Eleo-hyaul oa Smulao wh Fon omenaon, hnee Jounal of eonau., ol. 5, no. 6, ,. 9 T.. am,.. bul, Y.. hen, ae onolle alohm fo -DOF humano obo am, n Inenaonal onfeene on Syem-Ineae Inellene: hallene fo ou an ouon Enneen, oea Tehnoloy, , 4. ane onlne ublaon: 6 Noembe 6